Question

Can you please help with the following question with a picture demo??

Answer 1

Rate of change of elevation is `9/25` radians per second

Explanation:

The situation described in question is indicated in following picture, where after moving drone vertically up `x` feet, the angle `theta` is given by `theta=tan^(-1)(x/30)`

and as it is moving at `2(ft)/s` after `t` seconds, `theta` is given by

`theta=tan^(-1)((2t)/30)=tan^(-1)(t/15)`

and rate of change of elevation is

`(d theta(t))/(dt)=1/(1+(t/15)^2)=225/(225+t^2)`

and as it reaches `40` feet after `40/2=20` seconds, rate of change of elevation is given by

`(d theta(20))/(dt)=225/(225+400)=225/625=9/25` radians per second